Circumbinary Planetary Systems Research Articles

On the properties of free floating planets originating in circumbinary planetary systems

Abstract Free-floating planets are a new class of planets recently discovered. These planets don’t orbit within stellar systems, instead living a nomadic life within the galaxy. How such objects formed remains elusive. Numerous works have explored mechanisms to form such objects, but have not yet provided predictions on their distributions that could differentiate between formation mechanisms. In this work we form these objects within circumbinary systems, where these planets are readily formed and ejected through interactions with the central binary stars. We find significant differences between planets ejected through planet-planet interactions and those by the binary stars. The main differences that arise are in the distributions of excess velocity, where binary stars eject planets with faster velocities. These differences should be observable amongst known free-floating planets in nearby star-forming regions. We predict that targeted observations of directly imaged free-floating planets in these regions should be able to determine their preferred formation pathway, either by planet formation in single or multiple stellar systems, or through processes akin to star formation. Additionally the mass distributions of free-floating planets can yield important insights into the underlying planet populations. We find that for planets more massive than 20 M⊕, their frequencies are similar to those planets remaining bound and orbiting near the central binaries. This similarity allows for effective and informative comparisons between mass distributions from microlensing surveys, to those of transit and radial velocities. Ultimately, by observing the velocity dispersion and mass distribution of free-floating planets, it will be possible to effectively compare with predictions from planet formation models, and to further understand the formation and evolution of these exotic worlds.

Tilted Circumbinary Planetary Systems as Efficient Progenitors of Free-floating Planets

The dominant mechanism for generating free-floating planets has so far remained elusive. One suggested mechanism is that planets are ejected from planetary systems due to planet–planet interactions. Instability around a single star requires a very compactly spaced planetary system. We find that around binary star systems instability can occur even with widely separated planets that are on tilted orbits relative to the binary orbit due to combined effects of planet–binary and planet–planet interactions, especially if the binary is on an eccentric orbit. We investigate the orbital stability of planetary systems with various planet masses and architectures. We find that the stability of the system depends upon the mass of the highest-mass planet. The order of the planets in the system does not significantly affect stability, but, generally, the most massive planet remains stable and the lower-mass planets are ejected. The minimum planet mass required to trigger the instability is about that of Neptune for a circular orbit binary and a super-Earth of about 10 Earth masses for highly eccentric binaries. Hence, we suggest that planet formation around inclined binaries can be an efficient formation mechanism for free-floating planets. While most observed free-floating planets are giant planets, we predict that there should be more low-mass free-floating planets that are as of yet unobserved than higher-mass planets.

Constraining the formation history of the TOI-1338/BEBOP-1 circumbinary planetary system

ABSTRACT The recent discovery of multiple planets in the circumbinary system TOI-1338/BEBOP-1 raises questions about how such a system formed. The formation of the system was briefly explored in the discovery paper, but only to answer the question do current pebble accretion models have the potential to explain the origin of the system? We use a global model of circumbinary planet formation that utilizes N-body simulations, including prescriptions for planet migration, gas and pebble accretion, and interactions with a circumbinary disc, to explore the disc parameters that could have led to the formation of the TOI-1338/BEBOP-1 system. With the disc lifetime being the main factor in determining how planets form, we limit our parameter space to those that determine the disc lifetime. These are: the strength of turbulence in the disc, the initial disc mass, and the strength of the external radiation field that launches photoevaporative winds. When comparing the simulated systems to TOI-1338/BEBOP-1, we find that only discs with low levels of turbulence are able to produce similar systems. The radiation environment has a large effect on the types of planetary systems that form, whilst the initial disc mass only has limited impact since the majority of planetary growth occurs early in the disc lifetime. With the most TOI-1338/BEBOP-1 like systems all occupying similar regions of parameter space, our study shows that observed circumbinary planetary systems can potentially constrain the properties of planet forming discs.

Can a binary star host three giant circumbinary planets?

ABSTRACT We investigate the orbital stability of a tilted circumbinary planetary system with three giant planets. The planets are spaced by a constant number (Δ) of mutual Hill radii in the range Δ = 3.4–12.0 such that the period ratio of the inner pair is the same as that of the outer pair. A tilted circumbinary planetary system can be unstable even if the same system around a coplanar binary is stable. For an equal-mass binary, we find that the stability of a three-planet system is qualitatively similar to that of a two-planet system, but the three-planet system is more unstable in mean motion resonance regions. For an unequal-mass binary, there is significantly more instability in the three-planet system as the inner planets can undergo von Zeipel–Kozai–Lidov oscillations. Generally in unstable systems, the inner planets are more likely to be ejected than the outer planets. The most likely unstable outcome for closely spaced systems, with Δ ≲ 8, is a single remaining stable planet. For more widely separated systems, Δ ≳ 8, the most likely unstable outcome is two stable planets, only one being ejected. An observed circumbinary planet with significant eccentricity may suggest that it was formed from an unstable system. Consequently, a binary can host three tilted giant planets if the binary stars are close to equal mass and provided that the planets are well spaced and not close to a mean motion resonance.

Orbital stability of two circumbinary planets around misaligned eccentric binaries

ABSTRACT With n-body simulations, we investigate the stability of tilted circumbinary planetary systems consisting of two non-zero mass planets. The planets are initially in circular orbits that are coplanar to each other, as would be expected if they form in a flat but tilted circumbinary gas disc and decouple from the disc within a time difference that is much less than the disc nodal precession period. We constrain the parameters of stable multiple planet circumbinary systems. Both planet–planet and planet–binary interactions can cause complex planet tilt oscillations that can destabilize the orbits of one or both planets. The system is considerably more unstable than the effects of these individual interactions would suggest, due to the interplay between these two interactions. The stability of the system is sensitive to the binary eccentricity, the orbital tilt, and the semimajor axes of the two circumbinary planets. With an inner planet semimajor axis of $5\, a_{\rm b}$, where ab is the semimajor axis of the binary, the system is generally stable if the outer planet is located at $\gtrsim 8\, a_{\rm b}$, beyond the 2:1 mean motion resonance with the inner planet. For larger inner planet semimajor axis, the system is less stable because the von-Zeipel–Kozai–Lidov mechanism plays a significant role, particularly for low binary-eccentricity cases. For the unstable cases, the most likely outcome is that one planet is ejected and the other remains bound on a highly eccentric orbit. Therefore, we suggest that this instability is an efficient mechanism for producing free-floating planets.

Frame-Dragging in Extrasolar Circumbinary Planetary Systems

Extrasolar circumbinary planets are so called because they orbit two stars instead of just one; to date, an increasing number of such planets have been discovered with a variety of techniques. If the orbital frequency of the hosting stellar pair is much higher than the planetary one, the tight stellar binary can be considered as a matter ring current generating its own post-Newtonian stationary gravitomagnetic field through its orbital angular momentum. It affects the orbital motion of a relatively distant planet with Lense-Thirring-type precessional effects which, under certain circumstances, may amount to a significant fraction of the static, gravitoelectric ones, analogous to the well known Einstein perihelion precession of Mercury, depending only on the masses of the system’s bodies. Instead, when the gravitomagnetic field is due solely to the spin of each of the central star(s), the Lense-Thirring shifts are several orders of magnitude smaller than the gravitoelectric ones. In view of the growing interest in the scientific community about the detection of general relativistic effects in exoplanets, the perspectives of finding new scenarios for testing such a further manifestation of general relativity might be deemed worth of further investigations.

Lucky planets: how circum-binary planets survive the supernova in one of the inner-binary components

A planet hardly ever survives the supernova of the host star in a bound orbit, because mass loss in the supernova and the natal kick imparted to the newly formed compact object cause the planet to be ejected. A planet in orbit around a binary has a considerably higher probability to survive the supernova explosion of one of the inner binary stars. In those cases, the planet most likely remains bound to the companion of the exploding star, whereas the compact object is ejected. We estimate this to happen to \sim 1/33∼1/33 the circum-binary planetary systems. These planetary orbits tend to be highly eccentric (e \ {\raise-.5ex\hbox{>}}\ 0.9), and \sim 20∼20,% of these planets have retrograde orbits compared to their former binary. The probability that the planet as well as the binary (now with a compact object) remains bound is about ten times smaller (\sim 3\cdot 10^{-3}∼3⋅10−3). We then expect the Milky way Galaxy to host \ {\raise-.5ex\hbox{<}}\ 10 x-ray binaries that are still orbited by a planet, and \\ {\raise-.5ex\hbox{<}}\ 150 planets that survived in orbit around the compact object’s companion. These numbers should be convolved with the fraction of massive binaries that is orbited by a planet.

Orbital dynamics of two circumbinary planets around misaligned eccentric binaries

ABSTRACT We investigate the orbital dynamics of circumbinary planetary systems with two planets around a circular or eccentric orbit binary. The orbits of the two planets are initially circular and coplanar to each other, but misaligned with respect to the binary orbital plane. The binary–planet and planet–planet interactions result in complex planet tilt oscillations. We use analytical models and numerical simulations to explore the effects of various values of the planet semimajor axes, binary eccentricity, and initial inclination. Around a circular orbit binary, secular tilt oscillations are driven by planet–planet interactions and are periodic. In that case, planets undergo mutual libration if close together and circulation if far apart with an abrupt transition at a critical separation. Around an eccentric orbit binary, secular tilt oscillations are driven by both planet–planet interactions and binary–planet interactions. These oscillations generally display more than one frequency and are generally not periodic. The transition from mutual planet libration to circulation is not sharp and there is a range of separations for which the planets are on orbits that are sometimes mutually librating and sometimes circulating. In addition, at certain separations, there are resonances for which tilt oscillations are complicated but periodic. For planets that are highly misaligned with respect to an eccentric orbit binary, there are stationary (non-oscillating) tilt configurations that are generalizations of polar configurations for the single planet case. Tilt oscillations of highly inclined planets occur for initial tilts that depart from the stationary configuration.

On the Detection of Habitable Trojan Planets in the Kepler Circumbinary Systems

Abstract We present the results of a study of the prospect of detecting habitable Trojan planets in the Kepler Habitable Zone circumbinary planetary systems (Kepler-16, -47, -453, -1647, and -1661). We integrated the orbits of 10,000 separate N-body systems (N = 4, 6), each with a one Earth-mass body in a randomly selected orbit near the L 4 and L 5 Lagrangian points of the host HZ circumbinary planet. We find that stable Trojan planets are restricted to a narrow range of semimajor axes in all five systems and limited to small eccentricities in Kepler-16, -47, and -1661. To assess the prospect of the detection of these habitable Trojan planets, we calculated the amplitudes of the variations they cause in the transit timing of their host bodies. Results show that the mean amplitudes of the transit timing variations (TTVs) correlate with the mass of the transiting planet and range from 70 minutes for Kepler-16b to 390 minutes for Kepler-47c. Our analysis indicates that the TTVs of the circumbinary planets caused by these Trojan bodies fall within the detectable range of timing precision obtained from the Kepler telescope’s long-cadence data. The latter points to Kepler data as a viable source to search for habitable Trojan planets.

Will gravitational waves discover the first extra-galactic planetary system?

Gravitational waves have opened a new observational window through which some of the most exotic objects in the universe, as well as some of the secrets of gravitation itself, can now be revealed. Among all these new discoveries, we recently demonstrated15 that space-based gravitational wave observations will have the potential to detect a new population of massive circumbinary exoplanets everywhere inside our Galaxy. In this paper, we argue that these circumbinary planetary systems can also be detected outside the Milky Way, in particular within its satellite galaxies. Space-based gravitational wave observations might thus constitute the mean to detect the first extra-galactic planetary system, a target beyond the reach of standard electromagnetic searches.

Tidal Decay of Circumbinary Planetary Systems

Abstract It is shown that circumbinary planetary systems are subject to universal tidal decay (shrinkage of orbits), caused by the forced orbital eccentricity inherent to them. Circumbinary planets (CBPs) are liberated from parent systems when, owing to the shrinkage, they enter the circumbinary chaotic zone. On shorter timescales (less than the current age of the universe), the effect may explain, at least partially, the observed lack of CBPs of close-enough (with periods <5 days) stellar binaries; on longer timescales (greater than the age of the universe but well within stellar lifetimes), it may provide massive liberation of chemically evolved CBPs. Observational signatures of the effect may comprise (1) a prevalence of large rocky planets (super-Earths) in the whole population of rogue planets (if this mechanism were the only source of rogue planets); (2) a mass-dependent paucity of CBPs in systems of low-mass binaries: the lower the stellar mass, the greater the paucity.

On the Lack of Circumbinary Planets Orbiting Isolated Binary Stars

Abstract We outline a mechanism that explains the observed lack of circumbinary planets (CBPs) via coupled stellar–tidal evolution of isolated binary stars. Tidal forces between low-mass, short-period binary stars on the pre-main sequence slow the stellar rotations transferring rotational angular momentum to the orbit as the stars approach the tidally locked state. This transfer increases the binary orbital period, expanding the region of dynamical instability around the binary, and destabilizing CBPs that tend to preferentially orbit just beyond the initial dynamical stability limit. After the stars tidally lock, we find that angular momentum loss due to magnetic braking can significantly shrink the binary orbit, and hence the region of dynamical stability, over time, impacting where surviving CBPs are observed relative to the boundary. We perform simulations over a wide range of parameter space and find that the expansion of the instability region occurs for most plausible initial conditions and that, in some cases, the stability semimajor axis doubles from its initial value. We examine the dynamical and observable consequences of a CBP falling within the dynamical instability limit by running N-body simulations of circumbinary planetary systems and find that, typically, at least one planet is ejected from the system. We apply our theory to the shortest-period Kepler binary that possesses a CBP, Kepler-47, and find that its existence is consistent with our model. Under conservative assumptions, we find that coupled stellar–tidal evolution of pre-main sequence binary stars removes at least one close-in CBP in 87% of multi-planet circumbinary systems.

UNCOVERING CIRCUMBINARY PLANETARY ARCHITECTURAL PROPERTIES FROM SELECTION BIASES

ABSTRACT Studying newly discovered circumbinary planetary systems improves our understanding of planetary system formation. Learning the architectural properties of these systems is essential for constraining the different formation mechanisms. We first revisit the stability limit of circumbinary planets. Next, we focus on eclipsing stellar binaries and obtain an analytical expression for the transit probability in a realistic setting, where a finite observation period and planetary orbital precession are included. Our understanding of the architectural properties of the currently observed transiting systems is then refined, based on Bayesian analysis and a series of tested hypotheses. We find that (1) it is not a selection bias that the innermost planets reside near the stability limit for eight of the nine observed systems, and this pile-up is consistent with a log uniform distribution of the planetary semimajor axis; (2) it is not a selection bias that the planetary and stellar orbits are nearly coplanar (≲3°), and this—along with previous studies—may imply an occurrence rate of circumbinary planets similar to that of single star systems; (3) the dominance of observed circumbinary systems with only one transiting planet may be caused by selection effects; (4) formation mechanisms involving Lidov–Kozai oscillations, which may produce misalignment and large separation between planets and stellar binaries, are consistent with the lack of transiting circumbinary planets around short-period stellar binaries, in agreement with previous studies. As a consequence of (4), eclipse timing variations may better suit the detection of planets in such configurations.

On the stability of circumbinary planetary systems

The dynamics of circumbinary planetary systems (the systems in which the planets orbit a central binary) with a small binary mass ratio discovered to date is considered. The domains of chaotic motion have been revealed in the “pericentric distance–eccentricity” plane of initial conditions for the planetary orbits through numerical experiments. Based on an analytical criterion for the chaoticity of planetary orbits in binary star systems, we have constructed theoretical curves that describe the global boundary of the chaotic zone around the central binary for each of the systems. In addition, based on Mardling’s theory describing the separate resonance “teeth” (corresponding to integer resonances between the orbital periods of a planet and the binary), we have constructed the local boundaries of chaos. Both theoretical models are shown to describe adequately the boundaries of chaos on the numerically constructed stability diagrams, suggesting that these theories are efficient in providing analytical criteria for the chaoticity of planetary orbits.

Long-term eclipse timing of white dwarf binaries: an observational hint of a magnetic mechanism at work

We present a long-term programme for timing the eclipses of white dwarfs in close binaries to measure apparent and/or real variations in their orbital periods. Our programme includes 67 close binaries, both detached and semi-detached and with M-dwarfs, K-dwarfs, brown dwarfs or white dwarfs secondaries. In total, we have observed more than 650 white dwarf eclipses. We use this sample to search for orbital period variations and aim to identify the underlying cause of these variations. We find that the probability of observing orbital period variations increases significantly with the observational baseline. In particular, all binaries with baselines exceeding 10 yrs, with secondaries of spectral type K2 -- M5.5, show variations in the eclipse arrival times that in most cases amount to several minutes. In addition, among those with baselines shorter than 10 yrs, binaries with late spectral type (>M6), brown dwarf or white dwarf secondaries appear to show no orbital period variations. This is in agreement with the so-called Applegate mechanism, which proposes that magnetic cycles in the secondary stars can drive variability in the binary orbits. We also present new eclipse times of NN Ser, which are still compatible with the previously published circumbinary planetary system model, although only with the addition of a quadratic term to the ephemeris. Finally, we conclude that we are limited by the relatively short observational baseline for many of the binaries in the eclipse timing programme, and therefore cannot yet draw robust conclusions about the cause of orbital period variations in evolved, white dwarf binaries.

On possible circumbinary configurations of the planetary systems of α Centauri and EZ Aquarii

Possible configurations of the planetary systems of the binary stars α Cen A–BandEZAqr A–C are analyzed. The P-type orbits—circumbinary ones, i.e., the orbits around both stars of the binary, are studied. The choice of these systems is dictated by the fact that α Cen is closest to us in the Galaxy, while EZ Aqr is the closest system whose circumbinary planets, as it turns out, may reside in the “habitability zone.” The analysis has been performed within the framework of the planar restricted three-body problem. The stability diagrams of circumbinary motion have been constructed: on representative sets of initial data (in the pericentric distance–eccentricity plane), we have computed the Lyapunov spectra of planetary motion and identified the domains of regular and chaotic motion through their statistical analysis. Based on present views of the dynamics and architecture of circumbinary planetary systems, we have determined the most probable planetary orbits to be at the centers of the main resonance cells, at the boundary of the dynamical chaos domain around the parent binary star, which allows the semimajor axes of the orbits to be predicted. In the case of EZ Aqr, the orbit of the circumbinary planet is near the habitability zone and, given that the boundary of this zone is uncertain, may belong to it.

Kozai–Lidov cycles towards the limit of circumbinary planets

Abstract In this Letter, we answer a simple question: Can a misaligned circumbinary planet induce Kozai–Lidov cycles on an inner stellar binary? We use known analytic equations to analyse the behaviour of the Kozai–Lidov effect as the outer mass is made small. We demonstrate a significant departure from the traditional symmetry, critical angles and amplitude of the effect. Aside from massive planets on near-polar orbits, circumbinary planetary systems are devoid of Kozai–Lidov cycles. This has positive implications for the existence of highly misaligned circumbinary planets: an observationally unexplored and theoretically important parameter space.

BIRTH LOCATIONS OF THEKEPLERCIRCUMBINARY PLANETS

The Kepler mission has discovered about a dozen circumbinary planetary systems, all containing planets on ~ 1 AU orbits. We place bounds on the locations in the circumbinary protoplanetary disk, where these planets could have formed through collisional agglomeration starting from small (km-sized or less) planetesimals. We first present a model of secular planetesimal dynamics that accounts for the (1) perturbation due to the eccentric precessing binary, as well as the (2) gravity and (3) gas drag from a precessing eccentric disk. Their simultaneous action leads to rich dynamics, with (multiple) secular resonances emerging in the disk. We derive analytic results for size-dependent planetesimal eccentricity, and demonstrate the key role of the disk gravity for circumbinary dynamics. We then combine these results with a simple model for collisional outcomes and find that in systems like Kepler 16, planetesimal growth starting with 10-100 m planetesimals is possible outside a few AU. The exact location exterior to which this happens is sensitive to disk eccentricity, density and precession rate, as well as to the size of the first generation of planetesimals. Strong perturbations from the binary in the inner part of the disk, combined with a secular resonance at a few AU inhibit the growth of km-sized planetesimals within 2 - 4 AU of the binary. In situ planetesimal growth in the Kepler circumbinary systems is possible only starting from large (few-km-sized) bodies in a low-mass disk with surface density less than 500 g/cm^2 at 1 AU.

SPIRAL PATTERNS IN PLANETESIMAL CIRCUMBINARY DISKS

Planet formation scenarios and the observed planetary dynamics in binaries pose a number of theoretical challenges, especially in what concerns circumbinary planetary systems. We explore the dynamical stirring of a planetesimal circumbinary disk in the epoch when the gas component disappears. For this purpose, following theoretical approaches by Heppenheimer (1978) and Moriwaki and Nakagawa (2004), we develop a secular theory for the dynamics of planetesimals in circumbinary disks. If the binary is eccentric and its components have unequal masses, a spiral density wave is generated, engulfing the disk on the secular timescale, which may exceed 10^7 yr, depending on the problem parameters. The spiral pattern is transient; thus, its observed presence may betray system's young age. We explore the pattern both analytically and in numerical experiments. The derived analytical spiral is a modified lituus; it matches the numerical density wave in the gas-free case perfectly. Using the SPH scheme, we explore the effect of residual gas on the wave propagation.

ANALYTIC ORBIT PROPAGATION FOR TRANSITING CIRCUMBINARY PLANETS

The herein presented analytical framework fully describes the motion of coplanar systems consisting of a stellar binary and a planet orbiting both stars on orbital as well as secular timescales. Perturbations of the Runge-Lenz vector are used to derive short period evolution of the system, while octupole secular theory is applied to describe its long term behaviour. A post Newtonian correction on the stellar orbit is included. The planetary orbit is initially circular and the theory developed here assumes that the planetary eccentricity remains relatively small (e_2<0.2). Our model is tested against results from numerical integrations of the full equations of motion and is then applied to investigate the dynamical history of some of the circumbinary planetary systems discovered by NASA's Kepler satellite. Our results suggest that the formation history of the systems Kepler-34 and Kepler-413 has most likely been different from the one of Kepler-16, Kepler-35, Kepler-38 and Kepler-64, since the observed planetary eccentricities for those systems are not compatible with the assumption of initially circular orbits.